[U_OUT, C_OUT, SCALE, SEP, FERR, WR, WI, INFO] = slicot_sb03md(DICO, JOB, FACT, TRANA, A, U_IN, C_IN)
| Parameter | Description |
|---|---|
| DICO | Specifies the type of Lyapunov equation to be solved as follows: = 'C': continuous-time case; 'D': discrete-time case. |
| JOB | Specifies the computation to be performed: 'X': Compute the solution only;= 'S': Compute the separation only; = 'B': Compute both the solution and the separation. |
| FACT | Specifies whether or not the real Schur factorization of the matrix A is supplied on entry. = 'F': On entry, A and Q contain the factors from the real Schur factorization of the matrix A; = 'N': The Schur factorization of A will be computed and the factors will be stored in A and Q. |
| TRANA | Specifies the form of op(A) to be used: = 'N': op(A) = A (No transpose); = 'T': op(A) = A**T (Transpose); = 'C': op(A) = A**T (Conjugate transpose = Transpose). |
| A | the leading N-by-N part of this array must contain the matrix A. If FACT = 'F', then A contains an upper quasi-triangular matrix in Schur canonical form; the elements below the upper Hessenberg part of the array A are not referenced. |
| U_IN | If FACT = 'N', zeros(N, N); If FACT = 'F', then U is an input argument and on entry the leading N-by-N part of this array must contain the orthogonal matrix U of the real Schur factorization of A. |
| C_IN | With JOB = 'X' or 'B', the leading N-by-N part of this array must contain the symmetric matrix C. |
| Parameter | Description |
|---|---|
| U_OUT | if INFO = 0 or INFO = N+1, it contains the orthogonal N-by-N matrix from the real Schur factorization of A. |
| C_OUT | With JOB = 'X' or 'B', if INFO = 0 or INFO = N+1, the leading N-by-N part of C has been overwritten by the symmetric solution matrix X. |
| SCALE | The scale factor, scale, set less than or equal to 1 to prevent the solution overflowing. |
| SEP | If JOB = 'S' or JOB = 'B', and INFO = 0 or INFO = N+1, SEP contains the estimated separation of the matrices op(A) and -op(A)', if DICO = 'C' or of op(A) and op(A)', if DICO = 'D'. |
| FERR | If JOB = 'B', and INFO = 0 or INFO = N+1, FERR contains an estimated forward error bound for the solution X. |
| WR | If FACT = 'N', and INFO = 0 or INFO = N+1, WR contains the real parts of the eigenvalues of A. |
| WI | If FACT = 'N', and INFO = 0 or INFO = N+1, WI contains the imaginary parts of the eigenvalues of A. |
| INFO | = 0: successful exit; |
To solve for X either the real continuous-time Lyapunov equation
op(A)'*X + X*op(A) = scale*C
or the real discrete-time Lyapunov equation
op(A)'*X*op(A) - X = scale*C
and/or estimate an associated condition number, called separation, where op(A) = A or A' (A**T) and C is symmetric (C = C').
N = 3;
DICO = 'D';
FACT = 'N';
JOB = 'X';
TRANA = 'N';
A = [3.0 1.0 1.0;
1.0 3.0 0.0;
0.0 0.0 3.0];
U_IN = zeros(N, N);
C_IN = [25.0 24.0 15.0;
24.0 32.0 8.0;
15.0 8.0 40.0];
[U_OUT, C_OUT, SCALE, SEP, FERR, WR, WI, INFO] = slicot_sb03md(DICO, JOB, FACT, TRANA, A, U_IN, C_IN)| Version | Description |
|---|---|
| 1.0.0 | initial version |